Q: What are the factor combinations of the number 402,635,359?

 A:
Positive:   1 x 4026353597 x 5751933743 x 9363613301 x 1337659619 x 6504612161 x 1863194333 x 9292315127 x 26617
Negative: -1 x -402635359-7 x -57519337-43 x -9363613-301 x -1337659-619 x -650461-2161 x -186319-4333 x -92923-15127 x -26617


How do I find the factor combinations of the number 402,635,359?

Unfortunately, there's not simple formula to identifying all of the factors of a number and it can be a tedious process when trying to identify the divisors of larger numbers. To find the factor combinations of the number 402,635,359, it is easier to work with a table - it's called factoring from the outside in.

Outside in Factoring

We start by creating a table and writing 1 on the left side and then the number we're trying to find the factors for on the right side in a table. Then, below that, write the numbers as a negative as well.

1 402,635,359
-1 -402,635,359

Why are the negative numbers included?

When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 402,635,359.

Example:
1 x 402,635,359 = 402,635,359
and
-1 x -402,635,359 = 402,635,359
Notice both answers equal 402,635,359

With that explanation out of the way, let's continue. Next, we take the number 402,635,359 and divide it by 2:

402,635,359 ÷ 2 = 201,317,679.5

If the quotient is a whole number, then 2 and 201,317,679.5 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 402,635,359
-1 -402,635,359

Now, we try dividing 402,635,359 by 3:

402,635,359 ÷ 3 = 134,211,786.3333

If the quotient is a whole number, then 3 and 134,211,786.3333 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 402,635,359
-1 -402,635,359

Let's try dividing by 4:

402,635,359 ÷ 4 = 100,658,839.75

If the quotient is a whole number, then 4 and 100,658,839.75 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 402,635,359
-1 402,635,359
Keep dividing by the next highest number until you cannot divide anymore.

If you did it right, you will end up with this table:

17433016192,1614,33315,12726,61792,923186,319650,4611,337,6599,363,61357,519,337402,635,359
-1-7-43-301-619-2,161-4,333-15,127-26,617-92,923-186,319-650,461-1,337,659-9,363,613-57,519,337-402,635,359

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